The contamination in water bodies is a big threat to the environment to control the water pollution, a model study is conducted. The pollution model for a system of three lakes that are interconnected by channels is taken into account. Three input models (periodic, exponentially decaying, and linear) were solved by employing a variational iteration technique coupled with various types of multipliers. Identification of exact multipliers for $n{\rm th}$-order differential equations is also presented. All said models were examined mathematically. We noticed that exact Lagrange multipliers in the correction functional bring more accurate and efficient results that have been deliberated graphically. The results obtained via variational iteration method (VIM)-$\lambda_E,$ already published work and the Runge-Kutta method of order four provides an excellent agreement. Additionally, the use of exact Lagrange multipliers with other techniques may be extended to other dynamical problems.